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Evaluate the following definite integral to three significant digits. I have been using rule #int ((du)/u) = ln |u| + C # And come out with an answer of 0.546. The answer is 0.732?

#int_0^1 (dx)/(sqrt(3-2x^2))#

Answer 1

#1/sqrt2 sin^-1(sqrt(2/3))~~0.676# (to three significant digits)

#int_0^1 (dx)/(sqrt(3-2x^2)) = 1/sqrt2 int_0^1 (dx)/(sqrt(3/2-x^2)) = 1/sqrt2 sin^-1(sqrt(2/3)x)_0^1=1/sqrt2 sin^-1(sqrt(2/3))~~0.6755#

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Answer 2

Cameron Alexander

To evaluate the integral, we can apply the rule:

[ \int \frac{du}{u} = \ln|u| + C ]

If the answer you've obtained is different from 0.732, there might be an error in your calculation or approach. To confirm the correct answer, it's essential to review the steps of your integration and ensure accuracy. Additionally, using a calculator or computer algebra system can help verify the result.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.